Finished 33 and 34.

ipython/EulerProblem034.ipynb

@@ -0,0 +1,101 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Euler Problem 34\n",
+    "\n",
+    "145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.\n",
+    "\n",
+    "Find the sum of all numbers which are equal to the sum of the factorial of their digits.\n",
+    "\n",
+    "Note: as 1! = 1 and 2! = 2 are not sums they are not included."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The algorithm for checking if a number is curious should be efficient. The more difficult thing is to select the upper bound for the brute force. It can be seen that $9 999 999 < 9! * 7$. Hence we can select $10^7$ as our bound."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "from math import factorial\n",
+    "\n",
+    "def is_curious(n):\n",
+    "    s = sum([factorial(int(d)) for d in str(n)])\n",
+    "    return n == s\n",
+    "\n",
+    "assert(is_curious(145) == True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "s = sum([n for n in range(3, 10**7) if is_curious(n)])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "40730"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "assert(s == 40730)\n",
+    "s"
+   ]
+  }
+ ],
+ "metadata": {
+  "completion_date": "Mon, 12 Feb 2018, 17:57",
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.4"
+  },
+  "tags": [
+   "factorial",
+   "brute force"
+  ]
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}